Plane geometry is one of the top killer questions in A-Math as there are many things to prove in addition to the many lines, circles, triangles, angles …
Read about the post I wrote earlier What you need to know to do well in Plane Geometry Part 1
I must admit this question almost drives me to insanity ;-) but luckily I saw the light when I was on the verge of sane and insanity …
Question: Prove that a circle can be drawn passing through the points T,P,X and Q. [3 marks]
Let me know how you handle this question in the comments section. For those who wants the step by step solution, drop me a comment as well. I highly recommend that you think about this question first before asking for solution.
There are 2 strategies I have used to help me in this Plane Geometry question. Do you want to know? so that you can learn and use them in your own question.
Hint: You must use one of the properties of circles.
Update: Video solution Here
Hi,
I'm Ai Ling. I enjoy coaching students who have challenges with
understanding and scoring in 'O' Level A-Maths and E-Maths. 
I really donno, haha, so can you show the solutions?
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As PT and PQ are of equal length, PTQ is an isosceles triangle, thus the circle can be drawn passing through these points by circumscribing the triangle….
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Hi Always Lovely,
This one is indeed tough…yet to come out with my answers..
Rgds
Sean
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Hmm this question is difficult, don’t even know where to start. Mind revealing the solution?
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to add on my previous reply:QXPT is a cyclic quad because the opp <s = 180degrees…
hmm if its wrong may i have the solution :)
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<QXT = <QPT
<XQP = <XTP
<s in the same segment
sorry for double reply! :)
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@anjali: As this is a 3 marks proving question, you won’t get the full marks by stating the property of triangle PTQ. Nevertheless. good attempt :)
@Joscelin: Joscelin, you can’t begin with the circle already passes through the 4 points and make the conclusions as above. You have to prove your conclusions to be correct hence the 4 points pass through the circle. This is also the challenginng part of many students for a proving question but you got the main concept correct. Begin the proving with the fact that angles in the same segment are equal.
I have updated the solution here => http://singaporeolevelmaths.com/2008/10/11/video-solution-of-plane-geometry-question-plusstrategy-to-handle-angles/
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Angles XPT = Angles XQT = 90(tangent perpendicular to radius)
Using the property, Angles in a semicircle, a circle passing thru T, P, X and Q can be constructed with XT as a diameter.
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